%------------------------------------------------------------------------------
% File     : ePrincess---1.0
% Problem  : KLE150+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : ePrincess-casc -timeout=%d %s

% Computer : n023.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sun Jul 17 01:51:37 EDT 2022

% Result   : Theorem 2.89s 1.34s
% Output   : Proof 4.37s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14  % Problem  : KLE150+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.15  % Command  : ePrincess-casc -timeout=%d %s
% 0.14/0.36  % Computer : n023.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Thu Jun 16 07:39:20 EDT 2022
% 0.14/0.37  % CPUTime  : 
% 0.58/0.61          ____       _                          
% 0.58/0.61    ___  / __ \_____(_)___  ________  __________
% 0.58/0.61   / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.58/0.61  /  __/ ____/ /  / / / / / /__/  __(__  |__  ) 
% 0.58/0.61  \___/_/   /_/  /_/_/ /_/\___/\___/____/____/  
% 0.58/0.61  
% 0.58/0.61  A Theorem Prover for First-Order Logic
% 0.58/0.61  (ePrincess v.1.0)
% 0.58/0.61  
% 0.58/0.61  (c) Philipp Rümmer, 2009-2015
% 0.58/0.61  (c) Peter Backeman, 2014-2015
% 0.58/0.61  (contributions by Angelo Brillout, Peter Baumgartner)
% 0.58/0.61  Free software under GNU Lesser General Public License (LGPL).
% 0.58/0.61  Bug reports to peter@backeman.se
% 0.58/0.61  
% 0.58/0.61  For more information, visit http://user.uu.se/~petba168/breu/
% 0.58/0.61  
% 0.58/0.61  Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.68/0.66  Prover 0: Options:  -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.55/0.94  Prover 0: Preprocessing ...
% 1.95/1.17  Prover 0: Constructing countermodel ...
% 2.89/1.33  Prover 0: proved (676ms)
% 2.89/1.34  
% 2.89/1.34  No countermodel exists, formula is valid
% 2.89/1.34  % SZS status Theorem for theBenchmark
% 2.89/1.34  
% 2.89/1.34  Generating proof ... found it (size 16)
% 4.13/1.64  
% 4.13/1.64  % SZS output start Proof for theBenchmark
% 4.13/1.64  Assumed formulas after preprocessing and simplification: 
% 4.13/1.64  | (0)  ? [v0] :  ? [v1] :  ? [v2] :  ? [v3] : ( ~ (v3 = v2) & strong_iteration(v1) = v2 & multiplication(v0, zero) = v1 & addition(one, v1) = v3 &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (multiplication(v5, v6) = v8) |  ~ (multiplication(v4, v6) = v7) |  ~ (addition(v7, v8) = v9) |  ? [v10] : (multiplication(v10, v6) = v9 & addition(v4, v5) = v10)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] :  ! [v9] : ( ~ (multiplication(v4, v6) = v8) |  ~ (multiplication(v4, v5) = v7) |  ~ (addition(v7, v8) = v9) |  ? [v10] : (multiplication(v4, v10) = v9 & addition(v5, v6) = v10)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : (v8 = v5 |  ~ (strong_iteration(v4) = v5) |  ~ (star(v4) = v6) |  ~ (multiplication(v5, zero) = v7) |  ~ (addition(v6, v7) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v7, v6) = v8) |  ~ (multiplication(v4, v5) = v7) |  ? [v9] : (multiplication(v5, v6) = v9 & multiplication(v4, v9) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v7, v6) = v8) |  ~ (addition(v4, v5) = v7) |  ? [v9] :  ? [v10] : (multiplication(v5, v6) = v10 & multiplication(v4, v6) = v9 & addition(v9, v10) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v6, v4) = v7) |  ~ (addition(v7, v5) = v8) |  ~ leq(v8, v6) |  ? [v9] :  ? [v10] : (star(v4) = v9 & multiplication(v5, v9) = v10 & leq(v10, v6))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v5, v6) = v7) |  ~ (multiplication(v4, v7) = v8) |  ? [v9] : (multiplication(v9, v6) = v8 & multiplication(v4, v5) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v4, v7) = v8) |  ~ (addition(v5, v6) = v7) |  ? [v9] :  ? [v10] : (multiplication(v4, v6) = v10 & multiplication(v4, v5) = v9 & addition(v9, v10) = v8)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v4, v6) = v7) |  ~ (addition(v7, v5) = v8) |  ~ leq(v8, v6) |  ? [v9] :  ? [v10] : (star(v4) = v9 & multiplication(v9, v5) = v10 & leq(v10, v6))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (multiplication(v4, v6) = v7) |  ~ (addition(v7, v5) = v8) |  ~ leq(v6, v8) |  ? [v9] :  ? [v10] : (strong_iteration(v4) = v9 & multiplication(v9, v5) = v10 & leq(v6, v10))) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (addition(v7, v4) = v8) |  ~ (addition(v6, v5) = v7) |  ? [v9] : (addition(v6, v9) = v8 & addition(v5, v4) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] :  ! [v8] : ( ~ (addition(v6, v7) = v8) |  ~ (addition(v5, v4) = v7) |  ? [v9] : (addition(v9, v4) = v8 & addition(v6, v5) = v9)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (multiplication(v7, v6) = v5) |  ~ (multiplication(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] :  ! [v7] : (v5 = v4 |  ~ (addition(v7, v6) = v5) |  ~ (addition(v7, v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : (v6 = v5 |  ~ (addition(v4, v5) = v6) |  ~ leq(v4, v5)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (strong_iteration(v6) = v5) |  ~ (strong_iteration(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : (v5 = v4 |  ~ (star(v6) = v5) |  ~ (star(v6) = v4)) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (strong_iteration(v4) = v5) |  ~ (multiplication(v4, v5) = v6) | addition(v6, one) = v5) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (star(v4) = v5) |  ~ (multiplication(v5, v4) = v6) | addition(one, v6) = v5) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (star(v4) = v5) |  ~ (multiplication(v4, v5) = v6) | addition(one, v6) = v5) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (addition(v5, v4) = v6) | addition(v4, v5) = v6) &  ! [v4] :  ! [v5] :  ! [v6] : ( ~ (addition(v4, v5) = v6) | addition(v5, v4) = v6) &  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (multiplication(v4, one) = v5)) &  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (multiplication(one, v4) = v5)) &  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (addition(v4, v4) = v5)) &  ! [v4] :  ! [v5] : (v5 = v4 |  ~ (addition(v4, zero) = v5)) &  ! [v4] :  ! [v5] : (v5 = zero |  ~ (multiplication(zero, v4) = v5)) &  ! [v4] :  ! [v5] : ( ~ (strong_iteration(v4) = v5) |  ? [v6] :  ? [v7] : (star(v4) = v6 & multiplication(v5, zero) = v7 & addition(v6, v7) = v5)) &  ! [v4] :  ! [v5] : ( ~ (strong_iteration(v4) = v5) |  ? [v6] : (multiplication(v4, v5) = v6 & addition(v6, one) = v5)) &  ! [v4] :  ! [v5] : ( ~ (star(v4) = v5) |  ? [v6] : (multiplication(v5, v4) = v6 & addition(one, v6) = v5)) &  ! [v4] :  ! [v5] : ( ~ (star(v4) = v5) |  ? [v6] : (multiplication(v4, v5) = v6 & addition(one, v6) = v5)) &  ! [v4] :  ! [v5] : ( ~ (addition(v4, v5) = v5) | leq(v4, v5)))
% 4.13/1.68  | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields:
% 4.13/1.68  | (1)  ~ (all_0_0_0 = all_0_1_1) & strong_iteration(all_0_2_2) = all_0_1_1 & multiplication(all_0_3_3, zero) = all_0_2_2 & addition(one, all_0_2_2) = all_0_0_0 &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v1, v2) = v4) |  ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v4) = v5) |  ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v0, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ~ (addition(v3, v4) = v5) |  ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v1 |  ~ (strong_iteration(v0) = v1) |  ~ (star(v0) = v2) |  ~ (multiplication(v1, zero) = v3) |  ~ (addition(v2, v3) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (addition(v0, v1) = v3) |  ? [v5] :  ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v2, v0) = v3) |  ~ (addition(v3, v1) = v4) |  ~ leq(v4, v2) |  ? [v5] :  ? [v6] : (star(v0) = v5 & multiplication(v1, v5) = v6 & leq(v6, v2))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v0, v3) = v4) |  ~ (addition(v1, v2) = v3) |  ? [v5] :  ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v1) = v4) |  ~ leq(v4, v2) |  ? [v5] :  ? [v6] : (star(v0) = v5 & multiplication(v5, v1) = v6 & leq(v6, v2))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v1) = v4) |  ~ leq(v2, v4) |  ? [v5] :  ? [v6] : (strong_iteration(v0) = v5 & multiplication(v5, v1) = v6 & leq(v2, v6))) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ~ leq(v0, v1)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (strong_iteration(v2) = v1) |  ~ (strong_iteration(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (star(v2) = v1) |  ~ (star(v2) = v0)) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strong_iteration(v0) = v1) |  ~ (multiplication(v0, v1) = v2) | addition(v2, one) = v1) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (star(v0) = v1) |  ~ (multiplication(v1, v0) = v2) | addition(one, v2) = v1) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (star(v0) = v1) |  ~ (multiplication(v0, v1) = v2) | addition(one, v2) = v1) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2) &  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1)) &  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1)) &  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1)) &  ! [v0] :  ! [v1] : ( ~ (strong_iteration(v0) = v1) |  ? [v2] :  ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1)) &  ! [v0] :  ! [v1] : ( ~ (strong_iteration(v0) = v1) |  ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1)) &  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1)) &  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1)) &  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 4.37/1.70  |
% 4.37/1.70  | Applying alpha-rule on (1) yields:
% 4.37/1.70  | (2)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(v0, one) = v1))
% 4.37/1.70  | (3)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v1) = v4) |  ~ leq(v4, v2) |  ? [v5] :  ? [v6] : (star(v0) = v5 & multiplication(v5, v1) = v6 & leq(v6, v2)))
% 4.37/1.70  | (4)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (addition(v3, v2) = v1) |  ~ (addition(v3, v2) = v0))
% 4.37/1.70  | (5)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v0, v1) = v2) | addition(v1, v0) = v2)
% 4.37/1.70  | (6)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (addition(v1, v0) = v2) | addition(v0, v1) = v2)
% 4.37/1.70  | (7)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (multiplication(one, v0) = v1))
% 4.37/1.70  | (8)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v1, v2) = v4) |  ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v4) = v5) |  ? [v6] : (multiplication(v6, v2) = v5 & addition(v0, v1) = v6))
% 4.37/1.70  | (9)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (star(v0) = v1) |  ~ (multiplication(v0, v1) = v2) | addition(one, v2) = v1)
% 4.37/1.70  | (10)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v3, v0) = v4) |  ~ (addition(v2, v1) = v3) |  ? [v5] : (addition(v2, v5) = v4 & addition(v1, v0) = v5))
% 4.37/1.70  | (11)  ! [v0] :  ! [v1] : ( ~ (strong_iteration(v0) = v1) |  ? [v2] : (multiplication(v0, v1) = v2 & addition(v2, one) = v1))
% 4.37/1.70  | (12) multiplication(all_0_3_3, zero) = all_0_2_2
% 4.37/1.70  | (13)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v0, v3) = v4) |  ~ (addition(v1, v2) = v3) |  ? [v5] :  ? [v6] : (multiplication(v0, v2) = v6 & multiplication(v0, v1) = v5 & addition(v5, v6) = v4))
% 4.37/1.70  | (14)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, zero) = v1))
% 4.37/1.70  | (15)  ! [v0] :  ! [v1] : (v1 = v0 |  ~ (addition(v0, v0) = v1))
% 4.37/1.70  | (16)  ! [v0] :  ! [v1] : ( ~ (strong_iteration(v0) = v1) |  ? [v2] :  ? [v3] : (star(v0) = v2 & multiplication(v1, zero) = v3 & addition(v2, v3) = v1))
% 4.37/1.70  | (17)  ! [v0] :  ! [v1] : ( ~ (addition(v0, v1) = v1) | leq(v0, v1))
% 4.37/1.70  | (18)  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] : (multiplication(v1, v0) = v2 & addition(one, v2) = v1))
% 4.37/1.70  | (19)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (star(v2) = v1) |  ~ (star(v2) = v0))
% 4.37/1.70  | (20)  ! [v0] :  ! [v1] : (v1 = zero |  ~ (multiplication(zero, v0) = v1))
% 4.37/1.70  | (21)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (addition(v0, v1) = v3) |  ? [v5] :  ? [v6] : (multiplication(v1, v2) = v6 & multiplication(v0, v2) = v5 & addition(v5, v6) = v4))
% 4.37/1.71  | (22)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v1, v2) = v3) |  ~ (multiplication(v0, v3) = v4) |  ? [v5] : (multiplication(v5, v2) = v4 & multiplication(v0, v1) = v5))
% 4.37/1.71  | (23)  ! [v0] :  ! [v1] :  ! [v2] : (v2 = v1 |  ~ (addition(v0, v1) = v2) |  ~ leq(v0, v1))
% 4.37/1.71  | (24)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v2, v0) = v3) |  ~ (addition(v3, v1) = v4) |  ~ leq(v4, v2) |  ? [v5] :  ? [v6] : (star(v0) = v5 & multiplication(v1, v5) = v6 & leq(v6, v2)))
% 4.37/1.71  | (25)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (strong_iteration(v0) = v1) |  ~ (multiplication(v0, v1) = v2) | addition(v2, one) = v1)
% 4.37/1.71  | (26)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v3, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ? [v5] : (multiplication(v1, v2) = v5 & multiplication(v0, v5) = v4))
% 4.37/1.71  | (27)  ~ (all_0_0_0 = all_0_1_1)
% 4.37/1.71  | (28)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] :  ! [v5] : ( ~ (multiplication(v0, v2) = v4) |  ~ (multiplication(v0, v1) = v3) |  ~ (addition(v3, v4) = v5) |  ? [v6] : (multiplication(v0, v6) = v5 & addition(v1, v2) = v6))
% 4.37/1.71  | (29)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : (v4 = v1 |  ~ (strong_iteration(v0) = v1) |  ~ (star(v0) = v2) |  ~ (multiplication(v1, zero) = v3) |  ~ (addition(v2, v3) = v4))
% 4.37/1.71  | (30)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (multiplication(v0, v2) = v3) |  ~ (addition(v3, v1) = v4) |  ~ leq(v2, v4) |  ? [v5] :  ? [v6] : (strong_iteration(v0) = v5 & multiplication(v5, v1) = v6 & leq(v2, v6)))
% 4.37/1.71  | (31)  ! [v0] :  ! [v1] : ( ~ (star(v0) = v1) |  ? [v2] : (multiplication(v0, v1) = v2 & addition(one, v2) = v1))
% 4.37/1.71  | (32) addition(one, all_0_2_2) = all_0_0_0
% 4.37/1.71  | (33)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] :  ! [v4] : ( ~ (addition(v2, v3) = v4) |  ~ (addition(v1, v0) = v3) |  ? [v5] : (addition(v5, v0) = v4 & addition(v2, v1) = v5))
% 4.37/1.71  | (34)  ! [v0] :  ! [v1] :  ! [v2] :  ! [v3] : (v1 = v0 |  ~ (multiplication(v3, v2) = v1) |  ~ (multiplication(v3, v2) = v0))
% 4.37/1.71  | (35) strong_iteration(all_0_2_2) = all_0_1_1
% 4.37/1.71  | (36)  ! [v0] :  ! [v1] :  ! [v2] : (v1 = v0 |  ~ (strong_iteration(v2) = v1) |  ~ (strong_iteration(v2) = v0))
% 4.37/1.71  | (37)  ! [v0] :  ! [v1] :  ! [v2] : ( ~ (star(v0) = v1) |  ~ (multiplication(v1, v0) = v2) | addition(one, v2) = v1)
% 4.37/1.71  |
% 4.37/1.71  | Instantiating formula (11) with all_0_1_1, all_0_2_2 and discharging atoms strong_iteration(all_0_2_2) = all_0_1_1, yields:
% 4.37/1.71  | (38)  ? [v0] : (multiplication(all_0_2_2, all_0_1_1) = v0 & addition(v0, one) = all_0_1_1)
% 4.37/1.71  |
% 4.37/1.71  | Instantiating (38) with all_9_0_4 yields:
% 4.37/1.71  | (39) multiplication(all_0_2_2, all_0_1_1) = all_9_0_4 & addition(all_9_0_4, one) = all_0_1_1
% 4.37/1.71  |
% 4.37/1.71  | Applying alpha-rule on (39) yields:
% 4.37/1.71  | (40) multiplication(all_0_2_2, all_0_1_1) = all_9_0_4
% 4.37/1.71  | (41) addition(all_9_0_4, one) = all_0_1_1
% 4.37/1.71  |
% 4.37/1.71  | Instantiating formula (26) with all_9_0_4, all_0_2_2, all_0_1_1, zero, all_0_3_3 and discharging atoms multiplication(all_0_2_2, all_0_1_1) = all_9_0_4, multiplication(all_0_3_3, zero) = all_0_2_2, yields:
% 4.37/1.72  | (42)  ? [v0] : (multiplication(all_0_3_3, v0) = all_9_0_4 & multiplication(zero, all_0_1_1) = v0)
% 4.37/1.72  |
% 4.37/1.72  | Instantiating formula (6) with all_0_1_1, all_9_0_4, one and discharging atoms addition(all_9_0_4, one) = all_0_1_1, yields:
% 4.37/1.72  | (43) addition(one, all_9_0_4) = all_0_1_1
% 4.37/1.72  |
% 4.37/1.72  | Instantiating (42) with all_27_0_15 yields:
% 4.37/1.72  | (44) multiplication(all_0_3_3, all_27_0_15) = all_9_0_4 & multiplication(zero, all_0_1_1) = all_27_0_15
% 4.37/1.72  |
% 4.37/1.72  | Applying alpha-rule on (44) yields:
% 4.37/1.72  | (45) multiplication(all_0_3_3, all_27_0_15) = all_9_0_4
% 4.37/1.72  | (46) multiplication(zero, all_0_1_1) = all_27_0_15
% 4.37/1.72  |
% 4.37/1.72  | Instantiating formula (20) with all_27_0_15, all_0_1_1 and discharging atoms multiplication(zero, all_0_1_1) = all_27_0_15, yields:
% 4.37/1.72  | (47) all_27_0_15 = zero
% 4.37/1.72  |
% 4.37/1.72  | From (47) and (45) follows:
% 4.37/1.72  | (48) multiplication(all_0_3_3, zero) = all_9_0_4
% 4.37/1.72  |
% 4.37/1.72  | Instantiating formula (34) with all_0_3_3, zero, all_9_0_4, all_0_2_2 and discharging atoms multiplication(all_0_3_3, zero) = all_9_0_4, multiplication(all_0_3_3, zero) = all_0_2_2, yields:
% 4.37/1.72  | (49) all_9_0_4 = all_0_2_2
% 4.37/1.72  |
% 4.37/1.72  | From (49) and (43) follows:
% 4.37/1.72  | (50) addition(one, all_0_2_2) = all_0_1_1
% 4.37/1.72  |
% 4.37/1.72  | Instantiating formula (4) with one, all_0_2_2, all_0_1_1, all_0_0_0 and discharging atoms addition(one, all_0_2_2) = all_0_0_0, addition(one, all_0_2_2) = all_0_1_1, yields:
% 4.37/1.72  | (51) all_0_0_0 = all_0_1_1
% 4.37/1.72  |
% 4.37/1.72  | Equations (51) can reduce 27 to:
% 4.37/1.72  | (52) $false
% 4.37/1.72  |
% 4.37/1.72  |-The branch is then unsatisfiable
% 4.37/1.72  % SZS output end Proof for theBenchmark
% 4.37/1.72  
% 4.37/1.72  1102ms
%------------------------------------------------------------------------------